Bipartite Consensus on Matrix-Valued Weighted Networks
This brief examines bipartite consensus problem on matrix-valued weighted networks. First, it is shown that such networks achieve bipartite consensus if and only if the null space of the matrix-valued weighted Laplacian is spanned by a matrix-valued Gauge transformation, extending results for scalar...
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| Veröffentlicht in: | IEEE transactions on circuits and systems. II, Express briefs Express briefs, 2019-08, Vol.66 (8), p.1441-1445 |
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| container_title | IEEE transactions on circuits and systems. II, Express briefs |
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| creator | Pan, Lulu Shao, Haibin Mesbahi, Mehran Xi, Yugeng Li, Dewei |
| description | This brief examines bipartite consensus problem on matrix-valued weighted networks. First, it is shown that such networks achieve bipartite consensus if and only if the null space of the matrix-valued weighted Laplacian is spanned by a matrix-valued Gauge transformation, extending results for scalar-valued weighted networks. Second, it is shown that if a structurally balanced matrix-valued weighted network has a "positive-negative spanning tree," then the bipartite consensus can be achieved. Lastly, we show that in the case where edges are weighted by either positive definite or negative definite matrices, bipartite consensus is achieved if and only if the network is structurally balanced. Simulation results are provided to demonstrate these theoretical observations. |
| doi_str_mv | 10.1109/TCSII.2018.2884483 |
| format | Article |
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Simulation results are provided to demonstrate these theoretical observations.</description><subject>bipartite consensus</subject><subject>Couplings</subject><subject>Graph theory</subject><subject>Laplace equations</subject><subject>Mathematical analysis</subject><subject>Matrix methods</subject><subject>matrix-valued Guage transformation</subject><subject>Matrix-valued weighted networks</subject><subject>Networks</subject><subject>Null space</subject><subject>positive-negative spanning tree</subject><subject>Protocols</subject><subject>Simulation</subject><subject>Social networking (online)</subject><subject>structural balance</subject><subject>Symmetric matrices</subject><issn>1549-7747</issn><issn>1558-3791</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kMFOwzAQRC0EEqXwA3CJxDnFXtvJ-ggRhUoFDhQ4Wm66hZSSFNsR8PekpOK0c5g3Kz3GTgUfCcHNxax4nExGwAWOAFEplHtsILTGVOZG7G-zMmmeq_yQHYWw4hwMlzBg2VW1cT5WkZKiqQPVoQ1JUyd3LvrqO31265YWyQtVr2-xC_cUvxr_Ho7ZwdKtA53s7pA9ja9nxW06fbiZFJfTtASjY1rOkQvIOZDOwAk0XJFxBCgXc0dkyEkEV6IzOlNyTgsnwKlccylEprWSQ3be725889lSiHbVtL7uXlqADJU0HHXXgr5V-iYET0u78dWH8z9WcLv1Y__82K0fu_PTQWc9VBHRP4BaZ1yi_AWzeWA8</recordid><startdate>20190801</startdate><enddate>20190801</enddate><creator>Pan, Lulu</creator><creator>Shao, Haibin</creator><creator>Mesbahi, Mehran</creator><creator>Xi, Yugeng</creator><creator>Li, Dewei</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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First, it is shown that such networks achieve bipartite consensus if and only if the null space of the matrix-valued weighted Laplacian is spanned by a matrix-valued Gauge transformation, extending results for scalar-valued weighted networks. Second, it is shown that if a structurally balanced matrix-valued weighted network has a "positive-negative spanning tree," then the bipartite consensus can be achieved. Lastly, we show that in the case where edges are weighted by either positive definite or negative definite matrices, bipartite consensus is achieved if and only if the network is structurally balanced. 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| ispartof | IEEE transactions on circuits and systems. II, Express briefs, 2019-08, Vol.66 (8), p.1441-1445 |
| issn | 1549-7747 1558-3791 |
| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | bipartite consensus Couplings Graph theory Laplace equations Mathematical analysis Matrix methods matrix-valued Guage transformation Matrix-valued weighted networks Networks Null space positive-negative spanning tree Protocols Simulation Social networking (online) structural balance Symmetric matrices |
| title | Bipartite Consensus on Matrix-Valued Weighted Networks |
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